Calculus Examples

$lim_{x \to 2} \sqrt{x - 2}$

Step 1

Change the two-sided limit into a right sided limit.

$lim_{x \to 2^{+}} \sqrt{x - 2}$

Step 2

Evaluate the limit.

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Step 2.1

Move the limit under the radical sign.

$\sqrt{lim_{x \to 2^{+}} x - 2}$

Step 2.2

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $2$ .

$\sqrt{lim_{x \to 2^{+}} x - lim_{x \to 2^{+}} 2}$

Step 2.3

Evaluate the limit of $2$ which is constant as $x$ approaches $2$ .

$\sqrt{lim_{x \to 2^{+}} x - 1 \cdot 2}$

Step 3

Evaluate the limit of $x$ by plugging in $2$ for $x$ .

$\sqrt{2 - 1 \cdot 2}$

Step 4

Simplify the answer.

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Step 4.1

Multiply $- 1$ by $2$ .

$\sqrt{2 - 2}$

Step 4.2

Subtract $2$ from $2$ .

$\sqrt{0}$

Step 4.3

Rewrite $0$ as $0^{2}$ .

$\sqrt{0^{2}}$

Step 4.4

Pull terms out from under the radical, assuming positive real numbers.

$0$